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We consider a five-dimensional theory with a scalar fieldnon-minimally-coupled to gravity, and we look for novel black-string solutionsin the bulk. By appropriately choosing the non-minimal coupling function of thescalar field, we analytically solve the gravitational and scalar-fieldequations in the bulk to produce black-string solutions that describe aSchwarzschild-Anti-de Sitter space-time on the brane. We produce two completesuch solutions that are both characterised by a regular scalar field, alocalised-close-to-our brane energy-momentum tensor and a negative-definite,non-trivial bulk potential that may support by itself the warping of thespace-time even in the absence of the traditional, negative, bulk cosmologicalconstant. Despite the infinitely-long string singularity in the bulk, thefour-dimensional effective theory on the brane is robust with the effectivegravity scale being related to the fundamental one and the warping scale. It isworth noting that if we set the mass of the black hole on the brane equal tozero, the black string disappears leaving behind a regular brane-world modelwith only a true singularity at the boundary of the fifth dimension.

New Black-String Solutions for an Anti-de Sitter Brane in Scalar-Tensor Gravity